GATE Life Sciences Structure and Bonding Syllabus

What is resonance?

Resonance is the representation of a molecule whose true bonding cannot be shown by a single Lewis structure as a weighted combination (hybrid) of two or more valid contributing structures that differ only in the placement of electrons, not atoms.

How does resonance affect molecular stability and bond lengths?

Resonance delocalizes electrons, lowering the energy and stabilizing the molecule (resonance/delocalization energy). It also equalizes bond lengths; e.g., all six $\ce{C-C}$ bonds in benzene are identical, intermediate between single and double bonds.

List the criteria for a more stable (more contributing) resonance structure.

More stable structures have: (1) the maximum number of complete octets, (2) the maximum number of covalent bonds, (3) the least formal charge separation, and (4) negative formal charge on the more electronegative atom.

What is the formula for formal charge?

$$\text{Formal Charge} = V - N - \frac{B}{2}$$ where $V$ = valence electrons of the free atom, $N$ = non-bonding (lone-pair) electrons, and $B$ = bonding electrons shared by the atom.

Define dipole moment and give its formula and SI/conventional units.

Dipole moment is a vector measure of charge separation: $$\vec{\mu} = q \times d$$ where $q$ is the magnitude of charge and $d$ the distance between charges. It is measured in debye (D), where $1\ \text{D} = 3.336 \times 10^{-30}\ \text{C·m}$, and points from positive to negative.

Why is $\ce{CO2}$ nonpolar while $\ce{H2O}$ is polar, despite both having polar bonds?

In linear $\ce{CO2}$ the two $\ce{C=O}$ bond dipoles point in opposite directions and cancel, giving $\mu = 0$. In bent $\ce{H2O}$ the two $\ce{O-H}$ bond dipoles do not cancel and add to a net $\mu \approx 1.85\ \text{D}$.

How can the resultant dipole moment of two bond dipoles of magnitude $\mu_1$ and $\mu_2$ at angle $\theta$ be calculated?

$$\mu = \sqrt{\mu_1^{2} + \mu_2^{2} + 2\mu_1\mu_2\cos\theta}$$ For two equal dipoles $\mu_1=\mu_2=\mu_0$: $\mu = 2\mu_0\cos(\theta/2)$.

Why does $\ce{NH3}$ have a larger dipole moment than $\ce{NF3}$, even though F is more electronegative than H?

In $\ce{NH3}$ the lone-pair dipole and the $\ce{N-H}$ bond dipoles point in the same direction (reinforce), giving $\mu \approx 1.47\ \text{D}$. In $\ce{NF3}$ the $\ce{N-F}$ bond dipoles oppose the lone-pair dipole, partially cancelling, giving $\mu \approx 0.24\ \text{D}$.

Define bond length.

Bond length is the equilibrium internuclear distance between the nuclei of two covalently bonded atoms at which the potential energy of the system is minimum. It is typically expressed in picometres (pm) or angstroms ($1\ \text{Å} = 100\ \text{pm}$).

How does bond order relate to bond length and bond energy?

As bond order increases, bond length decreases and bond energy increases. Thus $\ce{C#C} < \ce{C=C} < \ce{C-C}$ in length, but the reverse order in strength.

Define bond angle.

Bond angle is the angle between two adjacent bonds (the lines joining the nuclei of two atoms bonded to a common central atom), measured at the central atom and expressed in degrees.

Define bond (dissociation) energy.

Bond dissociation energy is the energy required to break one mole of a particular bond in a gaseous molecule to give gaseous atoms/fragments (homolytically). It is endothermic and measured in $\text{kJ·mol}^{-1}$; larger values mean stronger bonds.

How does bond length generally vary as atomic size increases down a group?

Bond length increases down a group because the bonded atoms get larger (more shells), so the nuclei are farther apart; e.g., $\ce{H-F} < \ce{H-Cl} < \ce{H-Br} < \ce{H-I}$ in bond length, with correspondingly weaker bonds.

Define a hydrogen bond and state the atoms required.

A hydrogen bond is an attractive interaction between a hydrogen atom covalently bonded to a highly electronegative atom (F, O, or N) and a lone pair on another electronegative atom (F, O, or N). It is denoted $\ce{X-H\bond{...}Y}$ and has energy roughly $5$–$40\ \text{kJ·mol}^{-1}$.

Distinguish intermolecular from intramolecular hydrogen bonding, with an example of each.

Intermolecular H-bonding occurs between different molecules (e.g., in water, $\ce{HF}$, alcohols), raising boiling points and promoting association. Intramolecular H-bonding occurs within a single molecule (e.g., o-nitrophenol, salicylaldehyde), often lowering boiling point relative to the intermolecular-bonded isomer.

Why does water have an anomalously high boiling point and lower density as ice?

Extensive intermolecular hydrogen bonding requires extra energy to break, raising water's boiling point. In ice, each molecule H-bonds to four neighbors in an open tetrahedral lattice, creating empty space so ice is less dense than liquid water and floats.

Why is HF a weaker acid than HCl despite fluorine being more electronegative?

In aqueous HF, strong $\ce{F\bond{...}H-F}$ hydrogen bonding and the very strong $\ce{H-F}$ bond resist full ionization, so HF behaves as a weak acid, whereas HCl ionizes almost completely and is a strong acid.

What are van der Waals interactions, and what are their three main types?

Van der Waals interactions are weak, short-range intermolecular attractions arising from electrostatic interactions between molecules. The three types are: (1) Keesom forces (dipole–dipole), (2) Debye forces (dipole–induced dipole), and (3) London dispersion forces (induced dipole–induced dipole).

What are London dispersion forces and on what factors do they depend?

London (dispersion) forces are attractions between instantaneous induced dipoles caused by momentary fluctuations in electron distribution. They increase with molecular size/polarizability and surface area, so they grow with molar mass and are present in all molecules, including nonpolar ones.

How does the strength of van der Waals forces compare with that of hydrogen bonds and covalent bonds?

Strength order: covalent/ionic bonds (hundreds of $\text{kJ·mol}^{-1}$) $\gg$ hydrogen bonds ($\sim 5$–$40\ \text{kJ·mol}^{-1}$) $>$ van der Waals forces ($\sim 0.1$–$10\ \text{kJ·mol}^{-1}$). Van der Waals forces are the weakest.

How does the van der Waals attractive potential energy depend on intermolecular distance $r$?

The attractive part of the van der Waals (London dispersion) potential varies as $$U_{\text{attr}} \propto -\frac{1}{r^{6}}$$ making it short-ranged. In the Lennard-Jones model the full potential is $U(r) = 4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]$.

Define ionic radius.

Ionic radius is the effective distance from the nucleus of an ion to the edge of its electron cloud, i.e., the radius assigned to an ion in an ionic crystal (taken as its share of the internuclear distance between adjacent cation and anion).

How do the radii of cations and anions compare with their parent atoms?

A cation is smaller than its parent atom (loss of electrons reduces electron–electron repulsion and increases effective nuclear charge per electron), while an anion is larger than its parent atom (added electrons increase repulsion and shielding).

How does ionic radius vary across an isoelectronic series? Illustrate.

For isoelectronic species (same number of electrons), ionic radius decreases as nuclear charge increases. Example: $$\ce{N^{3-}} > \ce{O^{2-}} > \ce{F-} > \ce{Na+} > \ce{Mg^{2+}} > \ce{Al^{3+}}$$ all have 10 electrons but increasing $Z$.

How does ionic radius change down a group and across a period for ions of the same charge?

Down a group, ionic radius increases (more electron shells). Across a period, for cations of increasing charge it decreases due to rising effective nuclear charge; comparing same-charge cations across a period, radius decreases left to right.

Define lattice energy of an ionic crystal.

Lattice energy is the energy released when one mole of a solid ionic crystal is formed from its constituent gaseous ions (or, with opposite sign, the energy required to separate one mole of the solid into gaseous ions). It is a measure of the strength of ionic bonding.

According to the Born–Landé/Coulomb relationship, how does lattice energy depend on ionic charge and size?

Lattice energy is proportional to $$U \propto \frac{z_+ z_-}{r_+ + r_-}$$ so it increases with the product of ionic charges and decreases as the interionic distance (sum of ionic radii) increases. Thus $\ce{MgO}$ has a much larger lattice energy than $\ce{NaCl}$.

What is the Born–Landé equation for lattice energy?

$$U = -\frac{N_A M z_+ z_- e^{2}}{4\pi\varepsilon_0 r_0}\left(1 - \frac{1}{n}\right)$$ where $N_A$ is Avogadro's number, $M$ the Madelung constant, $z_\pm$ the ionic charges, $r_0$ the equilibrium interionic distance, and $n$ the Born exponent.

What is the Born–Haber cycle?

The Born–Haber cycle is a thermochemical cycle, based on Hess's law, that relates the lattice energy of an ionic solid to other measurable enthalpy changes (sublimation, ionization, dissociation, electron affinity, and formation), allowing lattice energy to be calculated indirectly.

Write the Born–Haber expression for the lattice energy $U$ of an ionic solid MX in terms of the standard enthalpy terms.

Applying Hess's law: $$\Delta H_f = \Delta H_{sub} + \tfrac{1}{2}\Delta H_{diss} + IE + EA + U$$ so the lattice energy is $$U = \Delta H_f - \Delta H_{sub} - \tfrac{1}{2}\Delta H_{diss} - IE - EA$$ where $IE$ is ionization energy of the metal and $EA$ the electron affinity of the non-metal.